My AMD GPU is not available in Cycle Render Preferences on version 2.8
Your graphics card doesn't meet the requirements for GPU rendering with Cycles as @DuaneDibbley already linked. The minimum requirements for the GPU are only for being able to run Blender at all.

For Blender 2.8 you will need GCN first generation or newer to run Blender. GCN second generation or newer is required for OpenCL GPU rendering.